The present invention relates to a system and method for automatic learning and rule induction from data. It could be applied to any situation where a cause and effect relationship between a plurality of input parameters and an output parameter, and historical data of the said input and output parameters is available. When applied to a process, the present invention relates to a system and method for monitoring and optimizing process quality control and, more particularly but not exclusively, to a system and method which employs an algorithm to provide a model useful for accurate and sensitive monitoring of a process, which enables detection of parameter(s) deviation even at early stages of a process.
In many areas and situations a cause and effect relationship between a plurality of input parameters and an output value exists. The present invention relates to a system and method for automatic learning and rule induction from data. More specifically, the present invention is a system and method to uncover the multivariate functional relationship between the input and output parameters. This function constitutes an empirical model of the relationship. It could be applied to any situation where historical data of input and output parameters is available. One of the areas that the present invention is applied is Process Quality Control. Traditionally, quality control of simple processes involves the classification of end products. In more complicated processes, which utilize numerous process stages, some quality control is affected in intermediate stages, involving the classification of intermediate products.
For example, in a chemical process, which includes numerous stages, inspection samples are typically drawn at random at various stages of the production line and inspected for being within predefined control limits.
A quality control methodology which is indicative of the quality of end products, is at times unacceptable for some processes since it cannot detect variabilities in intermediates produced.
Some processes, such as those employed by the semiconductor industry, utilize statistical process control (SPC), which uses control charts to analyze each major process stage and generate a predictable distribution chart for measured parameters (outputs) at each stage. A measured parameter which deviates from its distribution chart by more than, for example, three standard deviations is taken as indicative of process problems.
Although such quality control far supersedes that effected by sample inspection, it still suffers from several inherent limitations. The main reason is that the traditional SPC monitors an output with respect to the entire statistical distribution of this output. Each input combination defines a distribution of the related output, thus the overall distribution consists of many (sub) distributions.
By monitoring outputs with to their own specific distribution we achieve a much higher degree of accuracy. For example, the distribution charts of process outputs at various stages cannot detect undesirable combinations of input variables (e.g. such in which the unfavorable effect of the inputs on the monitored process output are mutually compensated), as long as the process outputs are within specifications. As a result, such quality control methodology cannot be utilized for early detection of variability in a process, nor can it be utilized to detect and point out deviations in individual variables, which may be important for understanding process related problems.
There is thus a widely recognized need for, and it would be highly advantageous to have, a system and method for process quality control devoid of the above limitations.
According to one aspect of the present invention there is provided a method of modeling a monitorable stage in a process, the method comprising the steps of: (a) measuring at least one input value of a parameter of the monitorable stage of the process; (a) measuring at least one output value of the parameter of the monitorable stage of the process; and (c) utilizing the at least one input value and the at least one output value for constructing a process output empirical model for uncovering a functional relationship between the at least one input value and at least one output value, the step of constructing the process output empirical modeler being effected by: (i) dividing at least one interval of the parameter into a plurality of sub intervals, such that each of the at least one interval is divided into at least two of the sub intervals; (ii) classifying the at least one output value according to the plurality of sub intervals, thereby presenting the at least one output value as a plurality of discrete variables defining the at least one output value; and (iii) using the plurality of discrete variables defining the at least one output value for defining the functional relationship between the at least one input value and the at least one output value, thereby modeling the monitorable stage of the process.
According to another aspect of the present invention there is provided a method of assessing the quality of a monitorable stage of a process, the method comprising the steps of: (a) constructing a process output empirical model for uncovering a functional relationship between an input value and an output value of a parameter of the monitorable stage of the process, the step of constructing a process output empirical model being effected by: (i) dividing at least one interval of the parameter into a plurality of sub intervals, such that each of the at least one interval is divided into at least two of the sub intervals; (ii) classifying at least one output value according to the plurality of sub intervals, thereby presenting the at least one output value as a plurality of discrete variables defining the at least one output value; and (iii) using the plurality of discrete variables defining the at least one output value for defining a functional relationship between at least one input value and at least one output value, thereby modeling the monitorable stage in the process; (b) applying the process output empirical model to a measured input value of the monitorable stage so as to predict a distribution of the output value of the monitorable stage; and (c) comparing a measured output value of the monitorable stage to the distribution of the output value of the monitorable stage predicted in step (b) to thereby assess the quality of the monitorable stage of the process.
According to yet another aspect of the present invention there is provided a system for assessing the quality of a process, the system comprising a data processing unit being for: (a) receiving a measured input value of a parameter of a monitorable stage of the process; (b) predicting a distribution of an output value of the parameter of the monitorable stage of the process according to the measured input value, the step of predicting being effected by a process output empirical model being executed by the data processing unit, the process output empirical model being generated by: (i) dividing at least one interval of the parameter into a plurality of sub intervals, such that each of the at least one interval is divided into at least two of the sub intervals; (ii) classifying at least one output value of the parameter according to the plurality of sub intervals, thereby presenting the at least one output value as a plurality of discrete variables defining the at least one output value; and (iii) using the plurality of discrete variables defining the at least one output value for defining the functional relationship between the at least one input value and at least one output value; and (c) comparing a measured output value of the parameter to the distribution of the output value of the parameter predicted in step (b), to thereby assess the quality of the monitorable stage of the process.
According to further features in preferred embodiments of the invention described below, each sub interval of the at least two sub intervals encompasses a non-overlapping subset of output values.
According to still further features in the described preferred embodiments the functional relationship is defined via a discrete function.
According to still further features in the described preferred embodiments the step of constructing the process output empirical modeler further includes the step of: (iv) statistically testing the discrete function for the goodness of the statistical result.
According to still further features in the described preferred embodiments the process is selected from the group consisting of a medical diagnostic process, a wafer production process and a trade order execution process.
According to still further features in the described preferred embodiments the monitorable stage of the process is a wafer chemical mechanical polishing stage of a wafer production process.
According to still further features in the described preferred embodiments the system further comprising at least one sensor being in communication with the data processing unit, the at least one sensor being for collecting data from the monitorable stage of the process, the data including the at least one input value and the at least one output value of the parameter.
According to yet an additional aspect of the present invention there is provided a method of assessing the quality of a monitorable stage of a process, the method comprising the steps of: (a) processing at least one output value of a parameter of the monitorable stage of the process so as to generate discrete variables representing the at least one output value; (b) defining a function for associating the discrete variables and at least one input value of the parameter of the monitorable stage of the process; (c) applying the function to a measured input value of the monitorable stage so as to predict a distribution of the output value of the monitorable stage; and (d) comparing a measured output value of the monitorable stage to the distribution of the output value of the monitorable stage predicted in step (c) to thereby assess the quality of the monitorable stage of the process.
According to still an additional aspect of the present invention there is provided a system for assessing the quality of a monitorable stage of a process, the system comprising a data processing unit being for: (a) processing at least one output value of a parameter of the monitorable stage of the process so as to generate discrete variables representing the at least one output value; (b) defining a function for associating the discrete variables and at least one input value of the parameter of the monitorable stage of the process; (c) applying the function to a measured input value of the monitorable stage so as to predict a distribution of the output value of the monitorable stage; and (d) comparing a measured output value of the monitorable stage to the distribution of the output value of the monitorable stage predicted in step (c) to thereby assess the quality of the monitorable stage of the process.
According to still further features in the described preferred embodiments the function is defined via non-parametric statistics.
According to still further features in the described preferred embodiments the function is a discrete function.
According to still further features in the described preferred embodiments the discrete variables are generated by dividing at least one interval of the parameter into a plurality of sub intervals and classifying the at least one output value according to the plurality of sub intervals.
According to still further features in the described preferred embodiments the system further comprising at least one sensor being in communication with the data processing unit, the at least one sensor being for collecting data from the monitorable stage of the process, the data including the at least one input value and the at least one output value of the parameter.
Embodiments of the invention address the shortcomings of the presently known configurations by providing a system and method for assessing the quality of at least one monitorable stage of a process thus enabling to optimize the process in a model which is useful for accurate and sensitive monitoring of the process. The model preferably enables detection of parameter(s) deviation even at early stages of the process